Inverse matrix - properties

Inverse matrix - methods of calculation

Use Gaussian elimination to calculate inverse matrix

Adjoin the identity matrix onto the right of the original matrix, so that you have A on the left side and the identity matrix on the right side. It will look like this [ A | I ].

Row-reduce the matrix until the left side to the Identity matrix. When the left side is the Identity matrix, the right side will be the Inverse [ I | A-1 ]. If you are unable to obtain the identity matrix on the left side, then the matrix is singular and has no inverse.

Take the augmented matrix from the right side and call that the inverse

Example 1.

Find the inverse matrix of the matrix A

A =

2

4

1

0

2

1

2

1

1

Solution: Adjoin the identity matrix onto the right of the matrix A:

A|E =

2

4

1

1

0

0

~

0

2

1

0

1

0

2

1

1

0

0

1

Row-reduce the matrix until the left side to the Identity matrix.
R3 - R1 → R3 (multiply 1 row by -1 and add it to 3 row):